The complete lecture — every idea is shown on the right with a real-life scene you already know: a labourer lifting bricks, a man shoving a wall, a roller-coaster, a porter's cart, the Tarbela turbine, and your own electricity meter. Scroll down, or press ▶ to have it narrated continuously while the panel keeps pace.
1 — What physics calls work: W = Fd cos θ
Holding a heavy bag while standing still feels like hard work — but in physics it is zero work, because nothing moved. Work is done only when a force produces a displacement.
- Work — W = Fd cos θ, where θ is the angle between the force and the displacement. It is the scalar (dot) product W = F · d.
- Joule (J) — 1 J = 1 N × 1 m; dimensions [ML²T⁻²]. Work is a scalar — magnitude and sign, no direction.
- Against gravity — lifting m through height h at steady speed needs a force mg, so W = mgh, and only the height counts, never the path: stairs, ramp or hoist all cost the same.
worked — hoisting bricks
A labourer raises a 25 kg brick load 8 m up a building (g = 9.8 m/s²).
W = mgh = 25 × 9.8 × 8 = 1960 J
2 — Positive, zero & negative work
The factor cos θ gives work its sign, and the sign says whether energy flows into the body or out of it — but first, if nothing moves there is no work at all, however hard you strain.
| Case | θ | Work | Example |
|---|
| Positive | 0° ≤ θ < 90° | W > 0 | horse pulling a cart; gravity on a falling mango |
| Zero (no motion) | d = 0 | W = 0 | pushing a fixed wall; holding a weight still |
| Zero (⟂) | θ = 90° | W = 0 | coolie walking with a load on his head; centripetal force on a satellite |
| Negative | 90° < θ ≤ 180° | W < 0 | friction on a sliding ball; gravity on a rising ball |
Exam point: a man pushing an immovable wall, or just holding 40 kg overhead, does zero physical work — no displacement, no work, no matter how tired he gets.
3 — Kinetic energy: KE = ½mv² (derivation)
Energy is the ability to do work; kinetic energy is the energy of motion. Start a mass m from rest with force F over distance d, reaching speed v:
Derivationv² = 0 + 2ad → d = v²/2a
W = Fd = (ma)(v²/2a) = ½mv² → KE = ½mv²
KE grows with the square of speed: double a car's speed and its braking energy — and roughly its braking distance — becomes four times larger.
worked — car KE
1200 kg car at 20 m/s, then 40 m/s.
½ × 1200 × 400 = 2.4 × 10⁵ J → at double speed 9.6 × 10⁵ J (4×)
4 — PE = mgh, work–energy theorem & conservation
Potential energy is stored by position: lifting m through h banks PE = mgh from a chosen reference level. A roller-coaster is the perfect demonstrator — winched up the first hill it stores PE, then trades it for KE in every dip and back to PE on every rise, the total staying fixed.
Work–energy theorem & conservationW(net) = ΔKE = ½mv² − ½mu²
(PE + KE) hilltop = (PE + KE) in the dip = constant
mgh = ½mv² → v = √(2gh) — independent of mass
With no friction the car would coast forever; in reality a little energy leaks to heat and sound each lap, so each hill must be lower than the last.
5 — Work at an angle: W = Fd cos θ
When the force is not along the motion, only its component along the displacement does work. A porter pulling a cart by an angled handle wastes the upward part of his pull — the cart only feels F cos θ along the road.
The master formulaW = F d cos θ = (F cos θ) × d
θ = 0° → W = Fd (maximum) · θ = 60° → half · θ = 90° → 0
worked — angled pull
A porter pulls a cart 8 m with a 50 N pull at 60° to the road.
W = 50 × 8 × cos 60° = 50 × 8 × 0.5 = 200 J
Two kinds of “work against”: against gravity W = mgh is stored as PE (path-free); against friction W = f·d is lost as heat (path-dependent) — which is why brake drums get hot.
6 — Forms of energy & its conservation
Energy can neither be created nor destroyed; it only changes form. At Tarbela Dam that whole chain runs in front of you: sunlight lifts sea water (solar → PE of clouds), rain fills the reservoir, falling water turns PE into KE, the turbine turns KE into rotational work, and the generator turns that into electrical energy that lights a bulb in Karachi.
- Mechanical — KE + PE: a speeding bus, water behind Tarbela, a drawn bow.
- Chemical → others — petrol → KE + heat in a rickshaw; food → muscle work; a dry cell → electrical energy.
- Electrical — moving charges: K-Electric supply, a phone charging.
Tarbela energy chainsolar → PE (reservoir) → KE (falling water) → work (turbine) → electrical → light/heat
capacity ≈ 4888 MW · total energy conserved at every arrow
7 — Power: the rate of doing work
Two porters lift identical trunks to the same floor — equal work — but the one who does it in half the time has twice the power. Power is energy delivered per second.
PowerP = W / t = energy per second · unit: watt (W) = J/s
P = Fd/t = Fv (constant force along motion)
1 kW = 10³ W · 1 MW = 10⁶ W · 1 hp = 746 W
worked — same work, different power
Two men each lift a 15 kg load 3 m (W = mgh = 441 J): one in 4 s, one in 8 s.
fast: 441/4 ≈ 110 W · slow: 441/8 ≈ 55 W — twice the power for half the time
8 — Efficiency, the kilowatt-hour & exam recap
No real machine turns all its input energy into useful output — friction and heat always take a cut. Efficiency = (useful output ÷ total input) × 100%: an electric motor ≈ 70–90%, a petrol engine ≈ 25–30%, human muscle ≈ 25%. The “lost” share is not destroyed — it becomes heat and sound, so conservation of energy still holds.
kW·h is ENERGY, not power1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J
energy (kWh) = power (kW) × time (h) — the “unit” on the K-Electric bill
worked — the AC bill
A 1.5 kW air-conditioner runs 6 h/night for 30 nights.
E = 1.5 × 180 = 270 kWh = 270 × 3.6 × 10⁶ = 9.72 × 10⁸ J
- W = Fd cos θ; joule = N·m; positive / zero (d = 0 or θ = 90°) / negative work.
- Against gravity W = mgh (path-free); against friction W = f·d (lost as heat).
- KE = ½mv² (from v² = 2ad); PE = mgh from a reference level.
- Work–energy theorem W(net) = ΔKE; conservation PE + KE = const; v = √(2gh).
- P = W/t = Fv; 1 hp = 746 W; efficiency = useful/total × 100%; 1 kWh = 3.6 × 10⁶ J.